CN114970121A - Generator-containing electromagnetic transient simulation iterative solution method and system - Google Patents
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Abstract
An electromagnetic transient simulation iterative solution method and system containing a generator comprises the following steps: establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator; dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation; carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step; according to the invention, through the integral differential equation of the column writing power system, the nonlinear equation is solved by using the Newton Raphson method, so that iterative solution of the motor and the circuit system in a time step can be realized, and the numerical divergence problem caused by separate solution delay of the motor and the circuit system or the numerical stability and precision problem caused by inaccurate prediction method are solved.
Description
Technical Field
The invention relates to the field of electromagnetic transient simulation of a power system, in particular to an electromagnetic transient simulation iterative solution method and system with a generator.
Background
In the existing electromagnetic transient simulation, a nonlinear element such as a generator is generally equivalent to a controlled source and a main circuit for connection calculation, and the value of the controlled source is generally updated by two ways. 1. Some unknown quantities at the t moment need to be predicted from the solution at the known t-delta t moment, the result accuracy depends on the adopted prediction method, and the numerical value is unstable due to improper selection of the prediction method; 2. by adopting the known quantity calculation at the time of t-delta t, the numerical divergence problem caused by time delay can exist, and the time delay needs to be compensated and corrected. Both of the above two methods have a problem of numerical stability, and the numerical stability can be further improved only by changing the solution method from direct solution to iterative solution in each time step.
Disclosure of Invention
In order to solve the problem of numerical stability of generator electromagnetic transient simulation in the prior art, the invention provides an electromagnetic transient simulation iterative solution method containing a generator, which comprises the following steps:
establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator;
dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation;
and carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step.
Preferably, the discretizing the unified nonlinear differential equation by an integration method to obtain a discretized equation includes:
converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
Preferably, the discretizing the first-order nonlinear differential equation by using different integration methods to obtain a discretized equation includes:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the equation obtained by multiplying the differential equation of the order of non-linearity by 1-beta at time t byAnd then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
Preferably, the unified non-linear differential equation is calculated as follows:
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
Preferably, the iteratively solving the discretized equation by using a newton iteration method to obtain a solution in each time step includes:
converting the discretized equation into a functional expression and acquiring a Jacobian matrix of the functional expression;
converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and carrying out iterative solution on the iterative formula by using a Newton iterative method to obtain a solution in each time step.
Preferably, the iterative solution of the iterative equation by using a newton iteration method to obtain a solution in each time step includes:
will | < f (x) N+1,k+1 ) II is and is providedComparing the determined error values, if the error values are smaller than the set error values, finishing the calculation, otherwise, solving according to an iterative expression of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
Preferably, the iteration formula using the newton iteration method is as follows:
in the formula, x N+1,k Is an initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
Based on the same inventive concept, the invention also provides an electromagnetic transient simulation iterative solution system with a generator, which comprises:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
Preferably, the discrete module of differential equations includes:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
Preferably, the discrete sub-modules are specifically configured to:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the formula obtained by multiplying the first-order nonlinear differential equation at the time t by 1-beta byAnd then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
Preferably, the unified non-linear differential equation is calculated as follows:
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
Preferably, the iterative solution module includes:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
Preferably, the solving submodule is specifically configured to:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the difference is less than the set error value, otherwise solving according to an iterative formula of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
Preferably, the iteration formula using the newton iteration method is as follows:
in the formula, x N+1 , k Is an initial estimate of time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
Compared with the prior art, the invention has the beneficial effects that:
an electromagnetic transient simulation iterative solution method and system containing a generator comprises the following steps: establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator; dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation; carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step; according to the invention, through the integral differential equation of the column writing power system, the nonlinear equation is solved by using the Newton Raphson method, so that iterative solution of the motor and the circuit system in a time step can be realized, and the numerical divergence problem caused by separate solution delay of the motor and the circuit system or the numerical stability and precision problem caused by inaccurate prediction method are solved.
Drawings
FIG. 1 is a flow chart of an electromagnetic transient simulation iterative solution method for a generator according to the present invention;
FIG. 2 is a flow chart of each time step iteration solution of the present invention.
Detailed Description
The invention provides an iterative solution method for generator-containing electromagnetic transient simulation, which aims at the problem of numerical stability existing when the electromagnetic transient simulation of a generator is equivalent to the connection of a controlled source and a circuit, establishes a unified differential equation between the generator and a circuit system, and carries out iterative solution on the integral equation by using a Newton-Raphson iteration method, thereby fundamentally avoiding the problem of numerical stability caused by the time delay or a prediction method when the generator is equivalent to the controlled source.
Example 1:
an electromagnetic transient simulation iterative solution method for a generator, the specific process of which is shown in fig. 1, comprises:
step 2, dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and 3, carrying out iterative solution on the dispersed equation by using a Newton iteration method to obtain a solution in each time step.
The following describes an iterative solution method for generator-containing electromagnetic transient simulation according to the present invention in detail with reference to fig. 2.
In step 1, establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator, specifically comprising:
differential equations in the time domain solution for column written power systems:
in the formula, K C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L For the inductance matrix, Ψ is the node flux linkage.
The extended column writes the differential equation containing the generator:
wherein n is the number of circuit nodes, and nm is the number of mass blocks of the mechanical shafting of the motor. L (theta) is a generator inductance matrix and is changed along with the rotation angle of the generator, and B is a generator winding and node correlation matrix. J is a generator shafting rotational inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, and T is a generator mechanical torque vector.
In step 2, dispersing the unified nonlinear differential equation by an integration method to obtain a dispersed equation, which specifically includes:
the electromagnetic transient simulation of the power system is to solve a differential equation shown in formula (2).
The equation (2) is a second order differential equation, and needs to be transformed into a first order differential equation for computer solution. Transforming equation (2) into:
discretizing equation (3) using different integration methods:
where Δ t is the discrete time step, x N Is the state quantity at time t, x N+1 Beta is a selection factor of different integration methods for the state quantity at the moment t + delta t. When beta is 0.5, the trapezoidal integration method is adopted; when β is 1, it is the receding euler method.
At time t, multiplying equation (3) by 1- β to obtain:
at time t + Δ t, β is multiplied by equation (3) to obtain:
calculating time t + delta t from time t, K 1 And K 2 Keeping the same, equation (5) and equation (6) are added to obtain:
equation (7) is subtracted from equation (8):
further simplified formula (9) is obtained:
Ax N+1 =Bx N +(1-β)R(x N )+βR(x N+1 ) (10)
due to R (x) in the formula (10) N ) And R (x) N+1 ) Is about x N And x N+1 So equation (10) is a non-linear equation.
In step 3, using a newton iteration method to iteratively solve the discretized equation to obtain a solution in each time step, specifically including:
the unknown variable in formula (10) is x N+1 And x is N And R (x) N ) Are all known amounts. In order to solve using the newton iteration method, equation (10) needs to be changed into the form of equation (11), i.e. to solve f (x) N+1 )=0。
f(x N+1 )=-Ax N+1 +Bx N +(1-β)R(x N )+βR(x N+1 )=0 (11)
Function f (x) N+1 ) The Jacobian matrix of:
wherein,
Γ(θ)= (L(θ)) -1 ,andare all matrix functions related to theta and can be specifically determined according to the type and parameters of the motor.
The iteration formula using the newton iteration method is:
wherein x N+1,k Is an initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration. When | f (x) N+1,k+1 ) When |, is less than the set allowable error, the iterative solution in each time step is completed.
Example 2:
an electromagnetic transient simulation iterative solution system with a generator, comprising:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
The discrete module of differential equations comprises:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a discrete equation.
The iterative solution module comprises:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
A differential equation establishing module, specifically configured to:
differential equations in the time domain solution for column written power systems:
in the formula, K C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L Psi is the node flux linkage.
The extended column writes the differential equation containing the generator:
wherein n is the number of circuit nodes, and nm is the number of mass blocks of the mechanical shafting of the motor. L (theta) is a generator inductance matrix which is changed along with the rotation angle of the generator, and B is a correlation matrix of the generator winding and the node. J is a generator shafting rotational inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, and T is a generator mechanical torque vector.
A conversion submodule, specifically configured to:
the electromagnetic transient simulation of the power system is to solve a differential equation shown in formula (2).
The equation (2) is a second order differential equation, and needs to be transformed into a first order differential equation for computer solution. Transforming equation (2) into:
discrete sub-modules, specifically configured to:
discretizing equation (3) using different integration methods:
where Δ t is the discrete time step, x N Is the state quantity at time t, x N+1 Beta is a selection factor of different integration methods for the state quantity at the moment t + delta tAnd (4) adding the active ingredients. When beta is 0.5, the method is a trapezoidal integration method; when β is 1, it is determined by the retropulsion euler method.
At time t, multiplying equation (3) by 1- β to obtain:
at time t + Δ t, β is multiplied by equation (3) to obtain:
calculating t + delta t time from t time, K 1 And K 2 Keeping the same, equation (5) and equation (6) are added to obtain:
equation (7) is subtracted from equation (8):
further simplified formula (9) is obtained:
Ax N+1 =Bx N +(1-β)R(x N )+βR(x N+1 ) (10)
due to R (x) in the formula (10) N ) And R (x) N+1 ) Is about x N And x N+1 So equation (10) is a non-linear equation.
A functional submodule, specifically configured to:
the unknown variable in formula (10) is x N+1 And x is N And R (x) N ) Are all known quantities. In order to solve using the newton iteration method, equation (10) needs to be changed into the form of equation (11), i.e. to solve f (x) N+1 )=0。
f(x N+1 )=-Ax N+1 +Bx N +(1-β)R(x N )+βR(x N+1 )=0 (11)
Function f (x) N+1 ) The Jacobian matrix of:
wherein,
Γ(θ)= (L(θ)) -1 ,andare all matrix functions related to theta and can be specifically determined according to the type and parameters of the motor.
The iterative sub-module is specifically configured to:
the iteration formula using the newton iteration method is:
wherein x N+1,k Is the initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
A solving submodule, specifically configured to:
when | f (x) N+1,k+1 ) When |, is less than the set allowable error, the iterative solution in each time step is completed.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The present invention is not limited to the above embodiments, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention are included in the scope of the claims of the present invention.
Claims (14)
1. An electromagnetic transient simulation iterative solution method for a generator, comprising:
establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator;
dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation;
and carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step.
2. The iterative solution method for generator-included electromagnetic transient simulation according to claim 1, wherein the discretizing the unified nonlinear differential equation by an integration method to obtain a discretized equation comprises:
converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
3. The iterative generator-based electromagnetic transient simulation solution method of claim 2, wherein discretizing the first-order nonlinear differential equation by different integration methods to obtain a discretized equation comprises:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
4. The iterative generator-based electromagnetic transient simulation solution method of claim 1, wherein the unified nonlinear differential equation is calculated as follows:
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is an incidence matrix of a generator winding and the nodes, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
5. The iterative solution method for generator-included electromagnetic transient simulation according to claim 1, wherein the iterative solution of the discretized equation by using a newton iteration method to obtain a solution in each time step comprises:
converting the discretized equation into a functional expression and acquiring a Jacobian matrix of the functional expression;
converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and carrying out iterative solution on the iterative formula by using a Newton iterative method to obtain a solution in each time step.
6. The iterative solution method for generator-included electromagnetic transient simulation according to claim 5, wherein the iterative solution of the iterative equation by using the newton iteration method to obtain a solution in each time step comprises:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the difference is less than the set error value, otherwise solving according to an iterative formula of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
8. An electromagnetic transient simulation iterative solution system with a generator, comprising:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
9. The iterative generator-based electromagnetic transient simulation solution system of claim 8, wherein the discrete differential equation module comprises:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a discrete equation.
10. The electromagnetic transient simulation iterative solution system with a generator of claim 9, wherein the discrete sub-modules are specifically configured to:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
11. The iterative generator-based electromagnetic transient simulation solution system of claim 8, wherein the unified differential equation is calculated as follows:
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L Is a matrix of inductance coefficients, and is,psi is the node flux linkage, theta is the motor shaft system rotation angle.
12. The generator-containing electromagnetic transient simulation iterative solution system of claim 8, wherein the iterative solution module comprises:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
13. The iterative generator-based electromagnetic transient simulation solving system of claim 12, wherein the solving submodule is specifically configured to:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the error value is smaller than the set error value, otherwise solving according to an iteration formula of a Newton iteration method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
14. The iterative generator-based electromagnetic transient simulation solution system of claim 12, wherein the iteration formula using the newton's iteration method is as follows:
in the formula, x N+1,k Is an initial estimate of time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
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CN116720338A (en) * | 2023-05-30 | 2023-09-08 | 杭州盛星能源技术有限公司 | Electromagnetic transient parallel iteration real-time simulation compensation method and device |
CN116720338B (en) * | 2023-05-30 | 2024-02-02 | 杭州盛星能源技术有限公司 | Electromagnetic transient parallel iteration real-time simulation compensation method and device |
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